K12a402
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+5 q^7-13 q^6+23 q^5-33 q^4+41 q^3-43 q^2+40 q-32+22 q^{-1} -12 q^{-2} +5 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-29 t^2+60 t-75+60 t^{-1} -29 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^4+1 }[/math] |
| Determinant | 271 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -4 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-9 z^4 a^{-2} +5 z^4 a^{-4} -z^4 a^{-6} +5 z^4-a^2 z^2-9 z^2 a^{-2} +6 z^2 a^{-4} -z^2 a^{-6} +5 z^2-3 a^{-2} +3 a^{-4} - a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-1} +3 z^{11} a^{-3} +21 z^{10} a^{-2} +12 z^{10} a^{-4} +9 z^{10}+10 a z^9+25 z^9 a^{-1} +36 z^9 a^{-3} +21 z^9 a^{-5} +5 a^2 z^8-21 z^8 a^{-2} +13 z^8 a^{-4} +21 z^8 a^{-6} -8 z^8+a^3 z^7-26 a z^7-82 z^7 a^{-1} -92 z^7 a^{-3} -24 z^7 a^{-5} +13 z^7 a^{-7} -13 a^2 z^6-48 z^6 a^{-2} -69 z^6 a^{-4} -30 z^6 a^{-6} +5 z^6 a^{-8} -27 z^6-2 a^3 z^5+21 a z^5+70 z^5 a^{-1} +61 z^5 a^{-3} -13 z^5 a^{-7} +z^5 a^{-9} +11 a^2 z^4+67 z^4 a^{-2} +59 z^4 a^{-4} +18 z^4 a^{-6} -2 z^4 a^{-8} +39 z^4+a^3 z^3-5 a z^3-19 z^3 a^{-1} -13 z^3 a^{-3} +5 z^3 a^{-5} +5 z^3 a^{-7} -3 a^2 z^2-26 z^2 a^{-2} -20 z^2 a^{-4} -6 z^2 a^{-6} -15 z^2+z a^{-1} +z a^{-3} -z a^{-5} -z a^{-7} +3 a^{-2} +3 a^{-4} + a^{-6} +2 }[/math] |
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